This is an announcement for the paper "Random processes via the
combinatorial dimension: introductory notes" by Mark Rudelson and Roman
Vershynin.
Abstract: This is an informal discussion on one of the basic problems
in the theory of empirical processes, addressed in our preprint
"Combinatorics of random processes and sections of convex bodies",
which is available at ArXiV and from our web pages.
Archive classification: Functional Analysis; Probability Theory
Mathematics Subject Classification: 46B09, 60G15, 68Q15
Remarks: 4 pages
The source file(s), rv-processes-description.tex: 12005 bytes, is(are)
stored in gzipped form as 0404193.gz with size 5kb. The corresponding
postcript file has gzipped size 30kb.
Submitted from: vershynin(a)math.ucdavis.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0404193
or
http://arXiv.org/abs/math.FA/0404193
or by email in unzipped form by transmitting an empty message with
subject line
uget 0404193
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get 0404193
to: math(a)arXiv.org.
This is an announcement for the paper "The numerical radius Haagerup
norm and Hilbert space square factorizations" by Takashi Itoh and
Masaru Nagisa.
Abstract: We study a factorization of bounded linear maps from an operator
space $A$ to its dual space $A^*$. It is shown that $T : A \longrightarrow
A^*$ factors through a pair of a column Hilbert spaces $\mathcal{H}_c$
and its dual space if and only if $T$ is a bounded linear form on $A
\otimes A$ by the canonical identification equipped with a numerical
radius type Haagerup norm. As a consequence, we characterize a bounded
linear map from a Banach space to its dual space, which factors through
a pair of Hilbert spaces.
Archive classification: Operator Algebras
Mathematics Subject Classification: 46L07 (Primary) 47L25, 46B28, 46L06
(Secontary)
Remarks: 16 pages
The source file(s), ina03.tex: 44003 bytes, is(are) stored in gzipped
form as 0404152.gz with size 12kb. The corresponding postcript file has
gzipped size 70kb.
Submitted from: itoh(a)edu.gunma-u.ac.jp
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.OA/0404152
or
http://arXiv.org/abs/math.OA/0404152
or by email in unzipped form by transmitting an empty message with
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uget 0404152
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to: math(a)arXiv.org.
This is an announcement for the paper "Ramsey and Nash-Williams
combinatorics via Schreier families" by Vassiliki Farmaki.
Abstract: The main results of this paper (a) extend the finite Ramsey
partition theorem, and (b) employ this extension to obtain a stronger
form of the infinite Nash-Williams partition theorem, and also a new
proof of Ellentuck's, and hence Galvin-Prikry's partition theorem. The
proper tool for this unification of the classical partition theorems at
a more general and stronger level is the system of Schreier families
$({\cal A}_{\xi})$ of finite subsets of the set of natural numbers,
defined for every countable ordinal $\xi$.
Archive classification: Functional Analysis
Mathematics Subject Classification: Primary 05D10; Secondary 05C55
Remarks: 28 pages, preliminary version
The source file(s), Ramseytheorem.tex: 91989 bytes, is(are) stored in
gzipped form as 0404014.gz with size 22kb. The corresponding postcript
file has gzipped size 83kb.
Submitted from: combs(a)mail.ma.utexas.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0404014
or
http://arXiv.org/abs/math.FA/0404014
or by email in unzipped form by transmitting an empty message with
subject line
uget 0404014
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to: math(a)arXiv.org.
